Note that the existence of such a Markov process comes for free in the
case when \(K(x,h)\)  is independent of \(x\) , see sec:levystuff. In
the general case it has been established by many authors in different general
contexts, see the discussion in [1]}. Denote by \(\tau _A=\inf \lbrace t>0|\,X_t\notin A\rbrace \) ,
\(T_A=\inf \lbrace t>0|\, X_t \in A\rbrace \)  the first exit time resp. hitting time
of the
process \(X\)  for a measurable set \(A\subset {\mathbb {R}}^d\) .
